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arXiv · 1907.03260

Strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients

Wei Liu·Michael Röckner·Xiaobin Sun·Yingchao Xie
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Abstract

This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally monotone coefficients and the fast component is a stochastic partial differential equations (SPDEs) with strongly monotone coefficients. The result is applicable to a large class of examples, such as the stochastic porous medium equation, the stochastic $p$-Laplace equation, the stochastic Burgers type equation and the stochastic 2D Navier-Stokes equation, which are the nonlinear stochastic partial differential equations. The main techniques are based on time discretization and the variational approach to SPDEs.

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Wei Liu, Michael Röckner, Xiaobin Sun, Yingchao Xie. 2019-07-07. Strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients. https://arxiv.org/abs/1907.03260

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